Abstract

The representation of rotation operators in the form of infinite tensor power series, R = exp(Ψ̂ ), has been found to be a valuable tool in multibody dynamics and nonlinear finite element analysis. This paper presents analogous formulations for the kinematic differential equations of the Euler-vector Ψ and elucidates their connection to Bernoulli-numbers. New power series such as the Bernoulli- and the Gibbs series are shown to provide compact expressions and a simple means for understanding and computing some of the fundamental formulae of rotational kinematics. The paper includes an extensive literature review, discussions of isogonal rotations, and a kinematic singularity measure.

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